Azumanga Daioh, K-On! Recommendations

Both are enjoyable slice-of-life comedies set in highschool starring an almost entirely female cast. Very similar humor and character types. Azumanga Daioh is a bit surreal at times and K-ON has the Moe-factor and a focus on music.

k-on and azumanga daioh is somewhat similar because they are bunch of/ group of girls having no similar personalities but they just get along well after that significant circumstances....they are all so funny LOL .. ^_^

Azumanga Daioh is a first generation school life anime. While not music-based and still random (seeing its a general school life genre), it has a more meaningful and funny storyline than K-ON! with a broader variety of characters.

Well, K-on! is more or less evolutioned azumanga. Both are moe-slice comedies, and K-on! is similar in a lot of small details like Mugi eyebrows=Chio pigtails and other stuff like that.
A lot of tempers remain the same also, Sawako is more or less equal to Yukari, for example.
Although K-on! has only one "salty" joke unlike azumanga, both shows remain a lot of similarities and if you liked one you should probably enjoy the other one.